When the condition of body is unaffected even though it is acted upon by no. of forces, it is said to be in equilibrium.
this PPT is about the general idea about Equilibrium of Forces. I will be uploading the numerical on it soon.
this is the PPT on first module of the engineering mechanics:
FORCE SYSTEM:
CONTENTS;
Introduction to Mechanics, Laws of mechanics, Newton's Laws, Law of Parallelogram, Law of transmissibility, Characteristics of force, System of Forces, Method of resolution and composition moment of a force,
Law of Moments, Varignon's Theorem, Problems on the moment, Resultant, Equivalent force& couple, properties of a couple
The following are the fundamental laws of mechanics:
(i) Newton’s first law
(ii) Newton’s second law
(iii) Newton’s third law
(iv) Newton’s gravitational law
(v) Law of transmissibility of forces
(vi) Parallelogram law of forces
Booster Questions???
1.What happens according to Newton if you let an untied balloon go????
2. Describe what happens if you are riding a skateboard and hit something (like a curb) with the front wheels???
3. Describe why you hold your gun next to your shoulder while deer hunting????
4. Why should we wear seatbelts – use one of Newton’s Laws in your answer?
5. How can Newton’s laws be used to explain how rockets are launched into space?
6. Explain how each of Newton’s laws affects a game of Tug of War.
Characteristics of force
Questions:
1. Define Mechanics. What are the different branches of mechanics?
2. What are the characteristics of force?
Force System
Coplanar
Concurrent
Collinear
Parallel
Like
Unlike
Non Concurrent & Non Parallel (General)
Non-coplanar
Concurrent
Collinear
Parallel
Like
Unlike
Non Concurrent & Non Parallel (General)
Forces added to obtain a single force which produces the same effect as the original system of forces.
This single force is known as Resultant force.
The process of finding the resultant force is called composition of forces.
There are two methods of finding resultant
Analytical method
Graphical method
Analytical methods are
Parallelogram law &
Method of Resolution
1. Resolution and composition of forces REV (2).pptVrushali Nalawade
Engineering Mechanics Unit-I
Force System
Composition and Resolution of Forces
Parallelogram Law
Varignon's Theorem
Moment
Newton's Law
Law of Moment
Branches of Mechanics
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
this is the PPT on first module of the engineering mechanics:
FORCE SYSTEM:
CONTENTS;
Introduction to Mechanics, Laws of mechanics, Newton's Laws, Law of Parallelogram, Law of transmissibility, Characteristics of force, System of Forces, Method of resolution and composition moment of a force,
Law of Moments, Varignon's Theorem, Problems on the moment, Resultant, Equivalent force& couple, properties of a couple
The following are the fundamental laws of mechanics:
(i) Newton’s first law
(ii) Newton’s second law
(iii) Newton’s third law
(iv) Newton’s gravitational law
(v) Law of transmissibility of forces
(vi) Parallelogram law of forces
Booster Questions???
1.What happens according to Newton if you let an untied balloon go????
2. Describe what happens if you are riding a skateboard and hit something (like a curb) with the front wheels???
3. Describe why you hold your gun next to your shoulder while deer hunting????
4. Why should we wear seatbelts – use one of Newton’s Laws in your answer?
5. How can Newton’s laws be used to explain how rockets are launched into space?
6. Explain how each of Newton’s laws affects a game of Tug of War.
Characteristics of force
Questions:
1. Define Mechanics. What are the different branches of mechanics?
2. What are the characteristics of force?
Force System
Coplanar
Concurrent
Collinear
Parallel
Like
Unlike
Non Concurrent & Non Parallel (General)
Non-coplanar
Concurrent
Collinear
Parallel
Like
Unlike
Non Concurrent & Non Parallel (General)
Forces added to obtain a single force which produces the same effect as the original system of forces.
This single force is known as Resultant force.
The process of finding the resultant force is called composition of forces.
There are two methods of finding resultant
Analytical method
Graphical method
Analytical methods are
Parallelogram law &
Method of Resolution
1. Resolution and composition of forces REV (2).pptVrushali Nalawade
Engineering Mechanics Unit-I
Force System
Composition and Resolution of Forces
Parallelogram Law
Varignon's Theorem
Moment
Newton's Law
Law of Moment
Branches of Mechanics
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
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Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
6. Unstable Equilibrium
• A body is said to be in unstable equilibrium if,
– An additional force is set up on slight
displacement which tends to push it away from
the original position of the body.
– It does not return back to its original position
after being slightly displaced by a force.
6
Prepared By: Prof. V.V.Nalawade
7. Neutral Equilibrium
• A body is said to be in neutral
equilibrium if,
–It is initially in a state of static equilibrium.
–No additional force is set up on slight
displacement from initial position.
–It occupies a new position and remains in
static equilibrium .
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8. Equilibrant
• It is the force which,
when applied to a body
acted by the concurrent
force system keeps the
body in equilibrium.
• Equilibrant is always equal
in magnitude and opposite
in direction & collinear to
resultant force.
Fx
Fy
R
E
8
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9. Analytical conditions of Equilibrium
• We know that magnitude of resultant of
forces is given by,
• Equilibrium means resultant force acting on
the body is ZERO, i.e. R=0
• Therefore, ΣFx = Σfy = 0
• Also the varignon’s theorem of moments
gives the position of the resultant,
• i.e. , ΣM = R* x but as R= 0; M = 0
2 2
x y
R F F
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Prepared By: Prof. V.V.Nalawade
10. Analytical conditions of
Equilibrium
• And hence the analytical conditions of
equilibrium are;
1. ΣFx = 0
2. Σfy = 0
3. ΣM = 0
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11. 1) Equilibrium of collinear force system
ΣF = 0
2) Equilibrium of concurrent force system
ΣFx = 0, ΣFy = 0
3) Equilibrium of parallel force system
ΣF = 0, ΣM = 0
4) Equilibrium of general force system
ΣFx = 0, ΣFy = 0, ΣM =0
11
Analytical conditions of Equilibrium
Prepared By: Prof. V.V.Nalawade
12. Free Body Diagram (FBD)
• FBD is a sketch of the body showing all active
and reactive forces acting on a body.
• Active forces means applied forces and
weight of the body
• Reactive forces means reactions offered by
floor, wall, strings, cables, supports etc
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Prepared By: Prof. V.V.Nalawade
13. Importance of FBD
• The sketch of FBD is the key step that
translates a physical problem into a form that
can be analyzed mathematically.
• The unknown forces of equilibrium of each
body can be obtained very easily.
• FBD represents all active and reactive forces.
• All equations of equilibrium can be applied to
each FBD separately.
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Prepared By: Prof. V.V.Nalawade
14. 1. Draw a neat sketch of the body assuming that all
supports are removed.
2. FBD may consists of an entire assembled structure or
any combination or part of it.
3. Show all the relevant dimensions & angles on the
sketch.
4. Show all the active forces on corresponding point of
application & insert their magnitude & direction if
known.
5. Show all the reactive forces due to each support.
6. If the sense of reaction is unknown, it should be
assumed.
7. Use principle of transmissibility wherever convenient.
Procedure of drawing FBD
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Prepared By: Prof. V.V.Nalawade
15. • Example 1:
1. Consider an electric lamp suspended by an
electric wire as shown in fig(a),
it is separated from its surrounding as shown in
fig(b).
In fig (c), active force (W) & reactive force (T),
acting on a free body are shown. Therefore fig
(C) is the FBD of fig (a).
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Prepared By: Prof. V.V.Nalawade
16. • Example 2:
1. A sphere suspended by a string but resting
against the wall as shown in fig(a),
it is separated from its surrounding as shown in
fig(b).
In fig (c), active force (W) & reactive force (TBC ,
RA), acting on a free body are shown.
(a) (b)
(c)
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Prepared By: Prof. V.V.Nalawade
17. • Example 3:
1. A sphere resting in a box as shown in fig(a),
it is separated from its surrounding as shown in
fig(b).
In fig (c), active force (W) & reactive force (RA &
RB =Reactions at contact points A & B), acting on
a free body are shown.
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Prepared By: Prof. V.V.Nalawade
18. • Example 4:
1. A block resting on horizontal floor as shown
in fig(a),
it is separated from its surrounding as shown in
fig(b).
In fig (c), active force (W) & reactive force (R
=Reaction offered by floor), acting on a free body
are shown.
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Prepared By: Prof. V.V.Nalawade
19. • Example 5:
1. A ladder having weight W resting against
rough horizontal surface & smooth vertical
wall as shown in fig(a),
In fig (b), active force (W) & reactive force (RA,
RB & F), acting on a free body are shown.
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Prepared By: Prof. V.V.Nalawade
21. • Example 8:
1. A ladder having weight W resting against
smooth horizontal surface & smooth vertical
wall as shown in fig(a),
In fig (b), active force (W) & reactive force (RA,
RB & F), acting on a free body are shown.
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Prepared By: Prof. V.V.Nalawade
22. Lami’s Theorem
• If three forces acting at a point on a body keep
it at rest, then each force is proportional to
the sine of the angle between other two
forces.
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Prepared By: Prof. V.V.Nalawade
25. 1. The theorem is applicable only if the body is
in equilibrium.
2. The theorem is not applicable for more or less
than three coplanar concurrent forces.
3. The theorem is applicable only if the nature of
all three forces are same, i.e. all forces are
either push or pull.
4. The theorem is not applicable for parallel or
non-concurrent forces.
5. The theorem is not applicable for non-
coplanar forces.
Limitations of Lami’s Theorem
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Prepared By: Prof. V.V.Nalawade
27. • Problem 1:
Find the tension in each
rope in fig.
• Solution:
Given Data: 1) Θ = Tan-1 4/3 = 53.13ᵒ
2) w =100 kg =10 x 9.81 = 981N
Step i) Consider the FBD of Point C.
θ1
θ2
θ3
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Prepared By: Prof. V.V.Nalawade
28. General Calculation :
Angle between W and TBC = 90 – 30 = 60ᵒ
Angle between TBC & TAC = 30 + 90 + (90 - 53.13)
=156.87ᵒ
Angle between TAC & W = 53.13 + 90 =143.13ᵒ
Step ii) Applying Lami’s Theorem,
θ1
θ2
θ3
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Prepared By: Prof. V.V.Nalawade
29. Types of
Support
Representa
tion
Reaction Reaction Force
Roller Vertical Reaction
Hinged Vertical as well
as Horizontal
Reaction
Fixed Vertical,
Horizontal
Reaction &
Moment
RA
RA
HA
RA
HA
MA 30
Prepared By: Prof. V.V.Nalawade
38. How to convert UDL in point load
• Intensity of UDL is in w
• We convert it into a point load by following
formula;
Where, w= intensity of UDL
l = span of UDL
And it is acting on a distance
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39. • A UDL is replaced by concentrated point
load.
• The magnitude of this equivalent point load
= the area under loading diagram and it
acts through the centroid.
• i.e. W = w * l 40
Prepared By: Prof. V.V.Nalawade
43. How to convert UVL in point load
• Intensity of UVL is in w
• We convert it into a point load by following
formula;
Where, w= intensity of UVL
l = span of UVL
And it is acting on a distance
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Prepared By: Prof. V.V.Nalawade
44. • A UVL is replaced by concentrated point
load.
• The magnitude of this equivalent point load
= the area under loading diagram and it
acts through the centroid.
• i.e. W = 1/2 * l * w 45
Prepared By: Prof. V.V.Nalawade
49. Simply Supported Beam
Simply Supported Beam With overhang
Cantilever Beam
Continuous Beam
Beams linked with internal hinges
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50. • Supported by a hinge at one end and roller at
the other end.
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51. • Beam projected beyond the supports at one
or both the ends.
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Prepared By: Prof. V.V.Nalawade
52. • A beam fixed at one end and free at other end
is called as cantilever beam.
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53. • A beam which has more than two supports is
called as continuous beam
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54. • When two or
more beams are
connected to
each other by
pin joint and
continuous
beam is
formed. Such a
joint are called
internal hinges.
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